Without seeing the part or a more detailed description of the problem, I am shooting in the dark. I have never had that problem. What version of Eagle are you using? Nevertheless, here are some thoughts.
I suspect you are trying to move it by clicking on it. Be sure all layers are shown. Can you see the little placement cross to click on? If not, maybe you constructed it way off that center. Put the part on a new schematic by itself and see what happens. Can you outline the part, then use the move dialog to move it? Step-by-step: click on move, then click on outline, outline the part to highlight it, then right click either inside or outside the highlight. You will see a difference, but either action should allow you to select move. Let us know what happens.
If all else fails, can you attach your part library here?
John